Newton's method for nonlinear mappings into vector bundles. Part II. Application to variational problems

Title data

Weigl, Laura ; Bergmann, Ronny ; Schiela, Anton:
Newton's method for nonlinear mappings into vector bundles. Part II. Application to variational problems.
Bayreuth , 2025 . - 27 p.
DOI: https://doi.org/10.48550/arXiv.2507.13836

Official URL:

Abstract in another language

We consider the solution of variational equations on manifolds by Newton's method. These problems can be expressed as root finding problems for mappings from infinite dimensional manifolds into dual vector bundles. We derive the differential geometric tools needed for the realization of Newton's method, equipped with an affine covariant damping strategy. We apply Newton's method to a couple of variational problems and show numerical results.

Further data

Item Type:	Preprint, postprint
Refereed:	Yes
Keywords:	Newton's method; Banach manifolds; vector bundles; variational problems
Subject classification:	MSC classes: 53-08, 46T05, 58E10, 49Q99
Institutions of the University:	Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics > Chair Applied Mathematics - Univ.-Prof. Dr. Anton Schiela Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT:	Yes
DDC Subjects:	500 Science > 510 Mathematics
Date Deposited:	30 Jul 2025 05:52
Last Modified:	30 Jul 2025 05:52
URI:	https://eref.uni-bayreuth.de/id/eprint/94385